基于密度法的传热结构拓扑优化设计

摘要

The topology optimization of variable density method was applied to heat transfer structure with complex construction,which is thought to be solved by traditional design method.Both the Dirichlet boundary and Neumann boundary conditions in steady-state heat conduction problems were considered.A topology optimization mathematical model based on the variable density method was developed,and the optimality criterion method satisfying the KKT (Karush-Kuhn-Tucker)condition was presented.Numerical examples with different boundary conditions were illustrated to verify the suggested approach.And the technique for eliminating numerical unstability,such as the checkerboard phenomenon,was also discussed. An example of thin walled tube shows that the method is also adapted to the three-dimensional problems.%传统的传热结构设计一般是基于热力学计算及工程经验，然而这种方法很难解决复杂边界条件的传热结构的设计问题。采用传热结构拓扑优化设计方法可有效解决传统设计方法难以解决的复杂边界问题。以密度法为基础，建立了散热弱度为目标函数的传热结构拓扑优化数学模型，推出了满足 KKT（Karush-Kuhn-Tucker）条件的最优准则法迭代公式。采用高阶单元的方法消除了优化过程中的数值不稳定现象。通过 Dirichlet 边界和 Neumann 边界不同组合下的数值算例，验证了算法的有效性。薄壁管的算例也表明，该算法也适用于三维壳体问题。